Question

The points $(-1,0)$ and $(-2,1)$ are the two extremities of a diagonal of a parallelogram. If $(-6,5)$ is the third vertex, then the fourth vertex of the parallelogram is

• A. $(2,-6)$
• B. $(2,-5)$
• C. $(3,-4)$
• D. $(-3,4)$
• E. $(3,-5)$

Answer 1

The correct option is C $(3,-4)$

Let the points of parallelogram are $A(-2,1),B(-6,5),C(-1,0)$ and $D(x,y)$
We know that, diagonals of parallelogram bisect each other
$(\frac{-2-1}{2},\frac{1+0}{2})=(\frac{x-6}{2},\frac{y+5}{2})$
$\Rightarrow \frac{-3}{2}=\frac{x-6}{2};\frac{1}{2}=\frac{y+5}{2}$
$\Rightarrow x=3;y=-4$
Thus the coordinates of fourth vertex of parallelogram are
$(3,-4)$